You live in a town with 300 adults and 200 children, and you are thinking about

Question

You live in a town with 300 adults and 200 children, and you are thinking about putting on a play to entertain your neighbors and make some money. A play has a fixed cost of $2000, but selling an extra ticket has zero marginal cost. Here are the demand schedules for your two types of customer

Price Adults Children
10 0 0
9 100 0
8 200 0
7 300 0
6 300 0
5 300 100
4 300 200
3 300 200
2 300 200
1 300 200

a. To maximize profit, what price would you charge for an adult ticket? For a child's ticket? How much profit do you make?
b. The city council passes a law prohibiting you from charging different prices to different customers. What price do you set for a ticket now? How much profit do you make?
c. Who is worse off because of the law prohibiting price discrimination? Who is better off? (If you can, quantify the changes in welfare.)
d. If the fixed cost of the play were $2,500 rather than $2,000 how would your answers to parts a, b, and c change?
0 300

Explanation / Answer

. $7 for an adult ticket and $4 for a child ticket. Profit is 7*300 + 4*200 - 2000 = 900.
b. Charge $7 per ticket. Profit is 7*300-2000 = 100.
c. The group producing the show is worse off, because their profits go down. Adult viewers stay stay same, since the same number of them get tickets at the same price. Child viewers are worse, since they no longer get to watch the show.
d. If the fixed cost were $2500, the producer of the show would still find in beneficial to do it under scenario a.), since he'd still be making a profit of $400. However, if we restrict him to charging the same price for kids and grown-ups, he'd be taking an economic loss, and he'd stop the show rather than doing any performances.

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